9 or 1?

Algebra Level 2

6 / 2 ( 1 + 2 ) = x , x = ? \large{6/2(1+2)=x \quad ,\quad x=?}

1 -9 9 -1

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1 solution

Isaac Wright
Jan 8, 2016

The handy order of operations rule you learned in grade school, PEMDAS, says you should solve a problem by working through the Parentheses, then the Exponents, the Multiplication and Division, followed by Addition and Subtraction. But the thing about PEMDAS is, some people interpret it different ways and in there lies the controversy behind this problem.

Some people think that anything touching a parentheses should be solved FIRST. Which means they simplify the problem as follows: 6÷2(1+2) = 6÷ 2(3) = 6÷6 = 1.

But just because a number is touching a parentheses doesn't mean it should be multiplied before division that's to the left of it. PEMDAS says to solve anything inside parentheses, then exponents, and then all multiplication and division from left to right in the order both operations appear (that's the key). That means that once you solve everything inside the parenthesis and simplify the exponents, you go from left to right no matter what. That means the problem should actually be solved as follows: 6÷2(1+2) = 6÷2 (1+2) = 6÷2 3 = 3*3 = 9.

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